1. Field of the Invention
The present invention relates to a method and a unit for computing a voltage drop of a battery to supply an electrical power to loads. More specifically, the voltage drop is divided along factors which are separately analyzed in use of a correlation between a discharge current and a terminal voltage (I-V) of the battery.
2. Related Art
Generally, a battery is repeatedly charged within its maximum charging capacity to discharge an electrical power to electrical equipment. The charging capacity decreases rapidly due to an excessive discharge or lack of an electrolyte and also decreases by an aged degradation of the battery. An excessive discharge of the battery, e.g. mounted on a motor vehicle will cause a starter motor not to be able to restart an engine when the battery is decreased in its discharging capacity due to its aged degradation.
An aged battery has a base resistance larger than that of a new battery. For determining replacement of a battery, a base resistance of the aged battery may be measured at a regular maintenance. The measured base resistance can show a degradation of the battery in consideration of a total resistance of the battery which is concluded from the base resistance. The total resistance includes a polarization resistance of the battery.
During discharging of the battery, a voltage drop between a pair of terminals of the battery is due to an inner impedance (combined resistance) of the battery. The voltage drop consists of an IR loss (base resistance, i.e. a voltage drop due to an ohmic resistance) and a voltage drop due to a polarization resistance (activation polarization and concentration polarization) related to a chemical reaction. As illustrated in FIG. 11 showing a correlation between a discharging current and a terminal voltage of a battery, the voltage drop of the IR loss varies linearly relative to a discharge current since a base resistance of the battery is constant.
In the meantime, a voltage drop due to a polarization resistance varies with the magnitude and elapsed time of a discharging current. Thus, a current-voltage correlation including a polarization resistance of the battery is necessary to be analyzed to know a present state of the battery.
Furthermore, it is desired to know an aged state of the battery while the battery is kept at a usage position.
In view of the aforementioned situation, an object of the invention is a method and a unit for computing a voltage drop of a battery to supply an electrical power to a load. The voltage drop is due to factors which are separately analyzed in use of a correlation between a discharge current and a terminal voltage (I-V) of the battery. The measurement of the discharge current and the terminal voltage can be made while the battery is kept at a usage position.
Another object of the invention is to provide a method and a unit for computing a voltage drop of the battery, in which a concentration polarization of the battery is separately obtained in use of a correlation between a discharge current and a terminal voltage (I-V) of the battery.
For achieving the objects, a first aspect of the invention is a method for computing a voltage drop divided along a plurality of factors for a battery to supply an electrical power to a load, the voltage drop being due to the factors which are separately analyzed in use of a correlation between a discharge current and a terminal voltage of the battery, the method comprising the steps of:
measuring cyclically a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in the load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases up to the peak,
obtaining a first approximate equation showing the correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing, and
calculating a voltage from each of the first and second approximate equations at a point where the discharge current is zero so that a deference between the two voltages at the point where the discharge current is zero is obtained,
wherein the deference is determined to be a total voltage drop due to a concentration polarization of the battery.
A second aspect of the invention is a method for computing a voltage drop divided along a plurality of factors for a battery to supply an electrical power to a load, the voltage drop being due to the factors which are separately analyzed in use of a correlation between a discharge current and a terminal voltage of the battery, the method comprising the steps of:
measuring cyclically a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in the load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases up to the peak,
obtaining a first approximate equation showing the correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing,
calculating a voltage from each of the first and second approximate equations at a point where the discharge current is zero so that a deference between the two voltages at the point where the discharge current is zero is obtained, wherein the deference is determined to be a total voltage drop due to a concentration polarization of the battery, and
calculating a voltage drop due to the concentration polarization from the total voltage drop at any point of the discharge current in use of a relation between the concentration polarization voltage drop and the discharge current with a corresponding discharging time, so that the concentration polarization voltage drop is obtained separately from a voltage drop due to the other factors. Note that the concentration polarization seems to occur with the rush current.
Preferably, a voltage drop due to the concentration polarization at any point of the discharge current is obtained from the total voltage drop due to the concentration polarization in use of a proportional relationship between the concentration polarization voltage drop and a corresponding discharging time elapsed before the point.
Preferably, the voltage drop due to the concentration polarization is obtained at the peak of the discharge current.
A third aspect of the invention is a method for computing a voltage drop divided along a plurality of factors for a battery to supply an electrical power to a load, the voltage drop being due to the factors which are separately analyzed in use of a correlation between a discharge current and a terminal voltage of the battery, the method comprising the steps of:
measuring cyclically a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in the load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases up to the peak,
obtaining a first approximate equation showing the correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing,
calculating a voltage from each of the first and second approximate equations at a point where the discharge current is zero so that a deference between the two voltages at the point where the discharge current is zero is obtained, wherein the deference is determined to be a total voltage drop due to a concentration polarization of the battery, and
calculating a voltage drop due to the concentration polarization from the total voltage drop at the peak of the discharge current in use of a proportional relationship between a concentration polarization voltage drop and a corresponding discharging elapsed time, so that the concentration polarization voltage drop is obtained separately from a voltage drop due to the other factors at the peak of the discharge current.
Preferably, a voltage drop due to the concentration polarization is obtained at any point of the discharge current from the concentration polarization voltage drop at the peak in use of a proportional relationship between the concentration polarization voltage drop and a corresponding elapsed time within the current increasing region up to the peak. Thus, the voltage drop due to the concentration polarization is obtained separately from a voltage drop due to the other factors at any point of the discharge current.
Preferably, a voltage drop due to the concentration polarization at any point of the discharge current within a current decreasing region after the peak is obtained from the voltage drop value at the peak in use of a proportional relationship between the concentration polarization voltage drop and a corresponding elapsed time at the time.
Preferably, voltage drop factors other than the concentration polarization are a base resistance and an activation polarization of the battery.
Preferably, a voltage drop due to factors other than the concentration polarization is obtained by deducting a voltage drop due to a concentration polarization of the battery from the first and second approximate equations so that first and second modified approximate equations are developed, and the first and second modified approximate equations are deducted respectively from the first and second approximate equations to provide first and second concentration polarization approximate equations. Thus, the first and second concentration polarization approximate equations can provide a voltage drop due to the concentration polarization at any point of the discharge current.
Preferably, an equation showing a voltage drop due to a base resistance of the battery is deducted respectively from the first and second modified approximate equations to obtain first and second activation polarization approximate equations showing a voltage drop due to an activation polarization of the battery. Thus, a voltage drop of the battery terminal is separated into each drop due to each of the base resistance, the concentration polarization, and the activation polarization.
Preferably, a voltage drop due to the concentration polarization of the battery is deducted from the first and second approximate equations to obtain first and second modified approximate equations, and at the peak of the rush current, a differential of the voltage relative to the current is obtained for each of the first and second modified approximate equations, wherein an intermediate value of thus obtained voltage differentials is determined as a base resistance of the battery. Thus, a voltage drop due to the base resistance is obtained separately from the other voltage drops.
Preferably, the obtained voltage differentials are averaged to obtain a base resistance of the battery.
Preferably, the obtained voltage differentials are averaged to determine a base resistance in consideration of time lengths of increasing and decreasing regions of the rush current. Thus, the base resistance is determined at the peak in consideration of effects of the concentration and activation polarizations.
Preferably, each of the first and second approximate equations is a quadratic equation. Thereby, the first modified approximate equation is also a quadratic equation which is appropriate for providing a voltage drop due to factors other than the concentration polarization.
Preferably, coefficients of the second approximate equation are determined from three voltage values between zero and the peak of the discharge current including the peak point. Thereby, the second modified approximate equation is obtained with ease.
Preferably, voltage differentials of the first and second modified approximate equations at the current peak are averaged to obtain the intermediate value. Thereby, a base resistance of the battery is obtained from the intermediate value with ease.
Preferably, an equation showing a voltage drop due to the base resistance of the battery is deducted respectively from the first and second modified approximate equations to obtain first and second activation polarization approximate equations showing a voltage drop due to an activation polarization of the battery. Thus, a voltage drop of the battery terminal is separated into each drop due to each of the base resistance, the concentration polarization, and the activation polarization.
A fourth third aspect of the present invention is a unit for computing a voltage drop divided along a plurality of factors for a battery to supply an electrical power to a load, the voltage drop being due to the factors which are separately analyzed in use of a correlation between a discharge current and a terminal voltage of the battery, the unit comprising:
a means for measuring cyclically a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in the load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases up to the peak,
a means for obtaining a first approximate equation showing the correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing,
a means for calculating a voltage from each of the first and second approximate equations at a point where the discharge current is zero so that a deference between the two voltages at the point where the discharge current is zero is obtained, wherein the deference is determined to be a total voltage drop due to a concentration polarization of the battery, and
a means for calculating a voltage drop due to the concentration polarization from the total voltage drop at any point of the discharge current in use of a relation between the concentration polarization voltage drop and the discharge current with a corresponding discharging time, so that the concentration polarization voltage drop is obtained separately from a voltage drop due to the other factors.
Preferably, a voltage drop due to the concentration polarization at any point of the discharge current is obtained from the total voltage drop due to the concentration polarization in use of a proportional relationship between the concentration polarization voltage drop and a corresponding discharging time elapsed before the point.
A fifth aspect of the present invention is a unit for computing a voltage drop divided along a plurality of factors for a battery to supply an electrical power to a load, the voltage drop being due to the factors which are separately analyzed in use of a correlation between a discharge current and a terminal voltage of the battery, the unit comprising:
a means for measuring cyclically a discharge current and a voltage between a pair of terminals of the battery while a rush current is flowing in the load electrically connected to the pair of the terminals, the rush current simply decreasing from a peak to a constant value after the rush current simply increases up to the peak,
a means for obtaining a first approximate equation showing the correlation between the current and the voltage in a region where the discharge current is increasing and a second approximate equation showing a correlation between the current and the voltage is obtained in a region where the discharge current is decreasing,
a means for calculating a voltage from each of the first and second approximate equations at a point where the discharge current is zero so that a deference between the two voltages at the point where the discharge current is zero is obtained, wherein the deference is determined to be a total voltage drop due to a concentration polarization of the battery, and
a means for calculating a voltage drop due to the concentration polarization from the total voltage drop at the peak of the discharge current in use of a proportional relationship between the concentration polarization voltage drop and a corresponding discharging time, so that the concentration polarization voltage drop is obtained separately from a voltage drop due to the other factors at the peak of the discharge current.